In a liquid chromatograph including a multichannel detector such as a PDA detector, an absorption spectrum is repeatedly acquired for sample solution eluted from the outlet of a column, with a time point of injecting a sample into a mobile phase regarded as a starting point, to obtain three dimensional chromatogram data in three dimensions: time, wavelength, and absorb (signal intensity). In a liquid chromatograph or a gas chromatograph including a mass spectrograph as a detector, namely a liquid chromatograph mass spectrograph or a gas chromatograph mass spectrograph, scan measurement is repeated within a predetermined mass-to-charge ratio range using the mass spectrograph to obtain three dimensional chromatogram data in three dimensions: time, mass-to-charge ratio, and signal intensity (ion intensity). In a comprehensive two-dimensional gas chromatograph or a comprehensive two-dimensional liquid chromatograph, further, three dimensional chromatogram data substantially in three dimensions: retention times and signal intensities in a first dimension column and a second-dimension column that have mutually different separate characteristics is obtained.
In the following, description will be made, by way of example, about a liquid chromatograph including a PDA detector (hereinafter, a liquid chromatograph including a PDA detector will be simply referred to as a liquid chromatograph unless particularly specified) as an analyzer with which three dimensional chromatogram data is obtained. It should be noted that the same discussion applies to liquid chromatograph mass spectrographs, gas chromatograph mass spectrographs, comprehensive two-dimensional liquid chromatographs, and comprehensive two-dimensional gas chromatographs as well.
FIG. 13A is a schematic diagram of three dimensional chromatogram data obtained with the liquid chromatograph described above. From the three dimensional chromatogram data, by extracting absorbance data at a specific wavelength (e.g., λ0) in a time direction, it is possible to create a wavelength chromatogram (hereinafter, simply referred to as a chromatogram) showing the relationship between measurement time point (i.e., retention time) and absorbance at the specific wavelength λ0 as illustrated in FIG. 13B. In addition, from the three dimensional chromatogram data, by extracting data representing absorbance at a specific time point (measurement time point) in a wavelength direction, it is possible to create an absorption spectrum (hereinafter, simply referred to as a spectrum) showing the relationship between wavelength and absorbance at the time point. In other words, the three dimensional chromatogram data illustrated in FIG. 13A can be considered to include spectrum information in the wavelength direction and chromatogram information in the time direction.
The quantity determination of a known target component contained in a sample with such a liquid chromatograph normally involves creating a chromatogram at an absorption wavelength at which the largest absorption of light by the target component appears. The quantity determination generally involves finding a starting point Ts and an ending point Te of a peak originating from the target component on the chromatogram, calculating the area value of the peak, and matching the peak area value with a calibration curve determined in advance so as to calculate a quantitative value.
When the quantity of a target component contained in the sample is determined, there is no problem when the peak that appears in the created chromatogram originates from only the target component. However, the peak does not always originate from a single component (target component), and it is often the case that a signal of an impurity out of the analyst's concern (broadly speaking, a component other than the target component) is included. If the analyst performs quantitative calculation without noticing it, the quantitative calculation lacks accuracy. Thus, prior to quantitative calculation, determination is normally made as to whether a peak appearing on a chromatogram originates from only a target component or includes another component, which is called peak purity determination. When a peak in question is overlapped with a peak originating from a component other than the target component, peak separation processing for separating the peak originating from the target component and the peak originating from the other component from each other is performed to obtain a highly pure peak originating from only the target component. Then the quantitative calculation is performed based on the peak.
As the peak purity determination processing and the peak separation processing, various techniques have been known and reduced to practical use.
For example, in the peak separation processing described in Patent Literature 1, when an analyst specifies an absorption wavelength of a target component, a differential value in the wavelength direction in the vicinity of the absorption wavelength is calculated for each of spectra that lines up in a time direction, and a differential chromatogram composed of the differential values arranged in the time direction is generated. If a peak appearing on the spectrum at the position of the absorption wavelength includes that of another component, the differential chromatogram is not flat but shows a peak. Thus, in accordance with whether a peak is present or absent on the differential chromatogram, determination is made as to whether the peak includes one originating from another component, and by making use of the waveform profile or the like of the peak on the differential chromatogram, the peaks of a plurality of components are separated from one another on a spectrum or a chromatogram.
However, such a technique requires an analyst to specify an absorption wavelength specific to a target component by themselves, which requires experience and skill to some extent of the analyst. In other words, manual operation by an analyst who is skilled in analyzing operation to some extent is necessary. In addition, although this method of peak separation processing can separate a peak of two components overlapping with one another, it is difficult to separate a peak of three or more components overlapping with one another.
Another well-known technique for the peak separation processing is a technique using deconvolution. For example, in the technique described in Patent Literature 2, an obtained chromatogram is subjected to deconvolution processing, multivariate analysis processing (factor analysis), or the like using a Gaussian function as a rough chromatogram waveform profile. From the result of the processing, a spectrum waveform with no overlap of components is first determined. Then, based on the obtained spectrum, a chromatogram waveform is estimated, and peaks on the chromatogram are separated from one another.
However, such a technique in which a spectrum is estimated first using the deconvolution processing, and then a chromatogram waveform is estimated using the estimated spectrum waveform involves a problem when a shoulder peak appears in the tailing of a chromatogram peak in that no solution is calculable in principle. This results in a failure to perform an appropriate peak separation. An example will be described with reference to FIG. 14A to FIG. 14D.
FIG. 14A illustrates a function including a shoulder peak expressed by exp(−x2)+0.1*exp(−(x−3)2), where x denotes a time on the horizontal axis. This waveform is multiplied by an impulse response expressed by exp(−x) illustrated in FIG. 14B, and a resultant waveform is illustrated in FIG. 14C. This waveform is subjected to ideal deconvolution processing using a Gaussian function, and a waveform illustrated in FIG. 14D is obtained. The waveform illustrated in FIG. 14D is not a simple decay curve. This indicates that even performing the deconvolution processing lets the component of a main peak be mixed in a spectrum at a retention time corresponding to the shoulder peak.
In the technique described in Patent Literature 2, in an estimation of a highly pure spectrum by excluding overlapping component, nonnegative limitation is imposed such that the elements of the spectrum are limited to positive values. However, the spectra obtained with a PDA detector, which can be regarded as multidimensional vectors, normally contain a lot of mutually dependent components. Thus, only by setting up a condition such as a simple nonnegative limitation, spectra originating from different components remain difficult to separate. In other words, without imposing limitation other than the nonnegative limitation that makes a chromatogram waveform profile natural (a waveform expected of a chromatogram), it is difficult to subtract only a spectrum component originating from a main peak from a spectrum observed at a retention time corresponding to the top of a shoulder peak.
For such reasons, the technique described in Patent Literature 2, as well as all techniques that employ procedures in which a pure spectrum is first estimated before the determination of a chromatogram waveform profile cannot handle a shoulder peak occurring in a tailing of a certain peak appropriately and is considered to be unsuitable for the separation of peaks in a chromatogram having such a waveform profile.